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Definte Integrals

  1. Sep 23, 2007 #1
    Definite Integrals

    I think I got these, but I left my text at work, so I was hoping someone could confirm that these answers are correct?

    a.)
    [tex]\int_{-1}^{1}\frac{dx}{1+x^2}[/tex]
    [tex]=\tan^{-1}(1)-\tan^{-1}(-1) =-\frac{\pi}{2}[/tex]

    and

    b.)
    [tex]\int_0^{\ln5}e^x(3-4e^x)[/tex]
    [tex]=\int_0^{\ln5}[3e^x-4e^{2x}]dx[/tex]
    [tex]=3e^x-2e^{2x}]_0^{\ln5}=49[/tex]

    Thanks,
    Casey
     
    Last edited: Sep 23, 2007
  2. jcsd
  3. Sep 23, 2007 #2

    Dick

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    No on both. You have a horrendous sign error on the first. On the second, it's just plain all wrong, even though the integration is correct. What gives?
     
  4. Sep 23, 2007 #3
    No sleep.

    The first one I am al effed up on...I thought arctan(1)=pi/4 and arctan(-1)=3pi/4 ?? my calculator is saying it is +pi/2 What does give?

    part 2....if the integration is correct, I don't know maybe I am putting it in the calculator wrong......maybe I should not need a calculator for this:rolleyes:..but I suck at powers of e....even though I know they are supposed to be easy.
     
  5. Sep 23, 2007 #4
    3e^{ln5)=15.....4e^{2ln5} is where I think I am messing it up...
    I do not remember how to evaluate.....

    ....4*ln25=100?
     
  6. Sep 23, 2007 #5
    [tex]\int_0^{\ln5}e^x(3-4e^x)[/tex]
    [tex]=\int_0^{\ln5}[3e^x-4e^{2x}]dx[/tex]
    [tex]=3e^x-2e^{2x}]_0^{\ln5}=86[/tex]


    Maybe?
     
  7. Sep 23, 2007 #6

    Dick

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    arctan(-1)=-pi/4. exp(2*ln(5))=5^2=25. Etc, etc. I think you need to get some sleep.
     
  8. Sep 23, 2007 #7
    Getting up at 3:30 am for work is not all it's cracked up to be. You are right though...my 24 hour streak is about over. In the AM I will need to look over that e to the ln crap.

    Thanks
     
  9. Sep 24, 2007 #8
    [tex]\int_0^{\ln5}e^x(3-4e^x)[/tex]
    [tex]=\int_0^{\ln5}[3e^x-4e^{2x}]dx[/tex]
    [tex]=3e^x-2e^{2x}]_0^{\ln5}=36[/tex]
    ....Can someone tell me if this is correct, or if I should just kill myself now :/

    Casey
     
  10. Sep 24, 2007 #9

    Gib Z

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    Closer, its actually -36. Get some sleep man, I remember once I stayed awake 30 hours, I walked home laughing at nothing...not a pretty sight for people walking by I'd imagine. Your not too far off insanity mate.
     
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